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Comparison results for M/G/1 queues with waiting and sojourn time deadlines

Part of: Special processes Computer system organization

Published online by Cambridge University Press:  30 July 2019

Yoshiaki Inoue
Yoshiaki Inoue*
Affiliation:
Osaka University
*
*Postal address: Department of Information and Communications Technology, Graduate School of Engineering, Osaka University, Suita 565-0871, Japan.
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Abstract

This paper considers two variants of M/G/1 queues with impatient customers, which are denoted by M/G/1+Gw and M/G/1+Gs. In the M/G/1+Gw queue customers have deadlines for their waiting times, and they leave the system immediately if their services do not start before the expiration of their deadlines. On the other hand, in the M/G/1+Gs queue customers have deadlines for their sojourn times, where customers in service also immediately leave the system when their deadlines expire. In this paper we derive comparison results for performance measures of these models. In particular, we show that if the service time distribution is new better than used in expectation, then the loss probability in the M/G/1+Gs queue is greater than that in the M/G/1+Gw queue.

Keywords

M/G/1 queueimpatient customervirtual waiting timeloss probabilitystochastic order

MSC classification

Primary: 60K25: Queueing theory
Secondary: 68M20: Performance evaluation; queueing; scheduling
Type
Research Papers
Information
Journal of Applied Probability , Volume 56 , Issue 2 , June 2019 , pp. 524 - 532
Copyright
© Applied Probability Trust 2019 

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